Argentinian Schwartzman was clearly being backed by a large South American and Spanish contingent on Court Suzanne Lenglen.
But the jeering of the world number one and defending champion seemed excessive and even prompted Eurosport's Alex Corretja to say: "I don't like that.
"It's Novak Djokovic. He has given us so much."
But Djokovic gave the perfect response with a 6-1 6-3 6-3 demolition of the 15th seed to book his place in the quarter-finals.
The Serbian has yet to drop a set in the tournament as he bids for a record-equalling 21st grand slam title.
"I think there's both cheering and a little bit of booing aswell. I don't like that. Come on, [it's] the world No 1. That's not respectful," she said, before adding: "It sounds like a football match now already the way they are screaming."
Former world No 2 Alex Corretja also criticised the fans.
"I don't like that. It's Novak Djokovic. He has given us so much."
The two-time French Open finalist also said: "Just support both and enjoy the match. I hate it when they don't respect the players or boo them."